To follow, to succeed, to be the successor of(verb)
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Use "come after" in a sentence
"Denny Moser, who during the last Seven had come after Fox with a pipe wrench and murder on his mind."
"The conversation revolved around general Norwegian-Israeli ties, but those of us who knew what was to come after the guests had taken their leave could think of nothing else."
"Rodes's division, less sharply organized, was under a man whose recent promotion had come after a clear demonstration of his capacity for command."